Question

the value of dy/dx for y =sin2x+cos2x is equal to​

Answer 1

Answer:

2cos2x-2sin2x

Step-by-step explanation:

y=sin2x+cos2x

let sin2x=u and cos2x=v

then, dy/dx=du/dx+dv/dx

first let us differentiate sin2x

u=sin2x,let 2x=t

by chain rule,

du/dx=d(sint)/dt* (dx/dt)

du/dx=2cos2x

similarly,

v=cos2x

dv/dx= -2sin2x(since differentiation of cosx is -sinx)

therefore, dy/dx=du/dx + dv/dx

dy/dx=2cos2x-2sin2x